Combine the milk and coffee beans in a medium saucepan and set over medium heat. Warm until small bubbles appear at the edges of the milk and it begins to steam, but do not bring to a boil.
Remove from heat and cover. Let sit for 1 hour at room temperature, or if you've got more time bring to room temperature and then chill in the fridge over night for a stronger coffee flavor.
Strain the coffee beans from the milk, pressing on the beans to get as much milk out as possible.
Return the milk to the saucepan and add the sugar and espresso powder. Set over medium heat and warm until small bubbles appear at the edges of the milk and it begins to steam, but do not bring to a boil.
In a bowl, whisk together the egg yolks. When the milk mixture is warm, slowly add it to the egg yolks while whisking constantly.
Pour the egg mixture back into the saucepan and cook over medium heat until it thickens and coats the back of a spoon, while whisking constantly.
Pour the mixture through a strainer and stir in the heavy cream and vanilla extract.
Chill the mixture thoroughly in the refrigerator for several hours, or overnight.
Freeze in an ice cream maker according to the manufacturer's instructions. Let the ice cream firm up in the freezer for a few hours before serving.